How out-group animosity can shape partisan divisions: A model of affective polarization

Abstract

Politically divided societies are also often divided emotionally: people like and trust those with similar political views (in-group favoritism) while disliking and distrusting those with different views (out-group animosity). This phenomenon, called affective polarization, influences individual decisions, including seemingly apolitical choices such as whether to wear a mask or what car to buy. We present a dynamical model of decision-making in an affectively polarized society, identifying three potential global outcomes separated by a sharp boundary in the parameter space: consensus, partisan polarization, and nonpartisan polarization. Analysis reveals that larger out-group animosity compared to in-group favoritism, i.e. more hate than love, is sufficient for polarization, while larger in-group favoritism compared to out-group animosity, i.e. more love than hate, is necessary for consensus. We also show that, counterintuitively, increasing cross-party connections facilitates polarization, and that by emphasizing partisan differences, mass media creates self-fulfilling prophecies that lead to polarization. Affective polarization also creates tipping points in the opinion landscape where one group suddenly reverses their trends. Our findings aid in understanding and addressing the cascading effects of affective polarization, offering insights for strategies to mitigate polarization.

Keywords: affective polarization; homophily; opinion dynamics; political psychology; social networks.

Fig. 1.

Phase diagram of the model (top) and four example trajectories. The four different regions of the phase diagram (defined by the ratio of in-group love to out-group hate and the ratio of group sizes) lead to different long-term outcomes in a fully connected network when both groups start from the same initial state (i.e. ${\theta }^{\mathcal{B}}(0)={\theta }^{\mathcal{R}}(0)$). The long-term outcomes are: (case 1, yellow) No Polarization, (case 2, red/case 3, blue) Partisan Polarization, and (case 4, green) Non-Partisan Polarization. Example trajectories in both time-domain and state space are shown below the phase diagram for ${\theta }^{\mathcal{B}}(0)={\theta }^{\mathcal{R}}(0)=0.8$. The blue and red color areas in state space indicate regions where ${\theta }^{\mathcal{B}}(t),{\theta }^{\mathcal{R}}(t)$ increase (i.e. regions where $p_{\theta }^{\mathcal{B}}(0\to 1)=1$ and $p_{\theta }^{\mathcal{R}}(0\to 1)=1$ according to Eq. 4). The black arrows in state space plots indicate the path of the differential equation Eq. 4. The purple arrows map the time domain trajectory to the state space.

Fig. 2.

An illustration of how decreasing homophily can cause a party-line polarization. Both figures correspond to $\alpha =0.8,\beta =0.7$ (larger in-group favoritism compared to out-group animosity) and $r=0.65$ (a majority red group). First row corresponds to a homophilic network (intergroup links are more likely to form than intragroup links) with $\rho =0.7$ whereas second row corresponds to an unbiased network (all links are equally likely to form). Note that decreasing ρ from 0.7 (homophily) to 0.5 (unbiased) increases the effect of out-group hate and decreases the effect of in-group love on the choices, and pushes the social network from case 1 (consensus) to case 3 (party-line polarization) in Fig. 1 (with x-axis re-scaled as $\frac{\alpha \rho }{\beta (1-\rho )}$).

Fig. 3.

An illustration of three cases where the two groups start at different initial states i.e. ${\theta }^{\mathcal{B}}(0)\ne {\theta }^{\mathcal{R}}(0)$, and one group reverses its direction. In cases i and ii, the minority blue group reverses its direction. In case iii, the majority red group reverses its direction. The blue and red lines in state space indicate the tipping points in opinion landscape where the respective group reverses its trend when the trajectory reaches it. The proposed model can demonstrate a variety of such phenomena when the initial states are different for the two groups.

Fig. 4.

The figure shows the trajectories of the model on an unbiased network (column 1—theoretical trajectories for the stochastic block model outlined in Dynamics of the model on a social network with communities section with $\rho =0.5$) and two real-world social networks (column 2—Facebook and column 3—Brightkite). Both groups start from the same initial state (${\theta }^{\mathcal{B}}(0)={\theta }^{\mathcal{R}}(0)$) and the model parameters ($\alpha ,\beta ,r$) for the four rows correspond to the four cases shown in Fig. 1. It can be seen that the theoretically predicted trajectory (column 1) closely resembles the trajectories for both real-world networks (columns 2 and 3) in each case.

Fig. 5.

The figure shows the trajectories of the model on an unbiased network (column 1—theoretical trajectories for the stochastic block model outlined in Dynamics of the model on a social network with communities section sec with $\rho =0.5$) and two real-world social networks (column 2—Facebook and column 3—Brightkite). The groups start from the different initial states (${\theta }^{\mathcal{B}}(0)\ne {\theta }^{\mathcal{R}}(0)$) and the model parameters ($\alpha ,\beta ,r$) for the three rows correspond to the three cases shown in Fig. 3. It can be seen that the theoretically predicted trajectory (column 1) closely resembles the trajectories for both real-world networks (columns 2,3) in each case.

Fig. 6.

The effect of homophily and heterophily on dynamics of affective polarization illustrated via the Facebook dataset with $\alpha =0.7,\beta =0.5$, and $r=0.53$. The homophilic (a), neutral (c) and heterophilic (e) node color assignments lead to three different behaviors. Compared to the dynamics under the neutral assignment (d), homophily facilitates consensus (b) and heterophily facilitates partisan polarization (f). This empirical result supports our theoretical finding that high exposure to the out-group can amplify party-line polarization.